One-dimensional textures and critical velocity in superfluid3He−A

Abstract

We study theoretically the stability of flow in superfluid ${}^{3}\mathrm{He}\ensuremath{-}\mathrm{A}.$ The calculations are done using a one-dimensional model where the order parameter depends only on the coordinate in the direction of the superfluid velocity ${\mathbf{v}}_{\mathrm{s}}.$ We concentrate on the case that the external magnetic field $\mathbf{H}$ is perpendicular to ${\mathbf{v}}_{\mathrm{s}},$ where only a few results are available analytically. We calculate the critical velocity ${v}_{c}$ at which the superflow becomes unstable against the formation of continuous vortices. The detailed dependence of ${v}_{c}$ on the temperature and on the form of the underlying orbital texture $\mathbf{l\ifmmode \hat{}\else \^{}\fi{}}(\mathbf{r})$ is investigated. Both uniform and helical textures of $\mathbf{l\ifmmode \hat{}\else \^{}\fi{}}$ and two types of domain-wall structures are studied. The results are partially in agreement with experiments made in a rotating cylinder.